There are many types of wallet. Can you be more specific? Also, define "withdraw"
Person A has an account in web app X and earned some 3 BTC over there. Now he wants to withdraw his BTC amount from web app's wallet to his own wallet. How can we automate this without any manual intervention ? Let us suppose the web app X's wallet is on blockchain.info, but person A's wallet may be anywhere. Person A will only provide his BTC address.
Yes you can do it because blockchain.info provides a transfer API. All you have to do is include the blockchain.info account credentials, pay amount, and destination address in an encrypted URL.
So for example you can set up a PHP server somewhere with a cron job scheduled to run once a week, once a day, whatever. When it runs it tells blockchain.info to send the desired amount to the desired address. The receiving address can be anywhere and that process would happen without humans (until the blockchain.info account balance was depleted).
Great - finally a definitive answer